A ladder rests against a frictionless vertical wall, with its upper end $6\,m$ above the ground and the lower end $4\,m$ away from the wall. The weight of the ladder is $500 \,N$ and its C. G. at $1/3^{rd}$ distance from the lower end. Wall's reaction will be, (in Newton)

If the block $A$ & $B$ are moving towards each other with acceleration $a$ and $b$. Find the net acceleration of $C$.

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then If $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface, then identify the correct statements

Two blocks of same mass $(4\ kg)$ are placed according to diagram. Initial velocities of bodies are $4\ m/s$ and $2\ m/s$ and the string is taut. Find the impulse on $4\ kg$ when the string again becomes taut  .......... $N-s$

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.